Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
394 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#13063443 | C2 | semidirect |
| 2. #26012525 | C2 | semidirect |
| 3. #26012510 | C2 | semidirect |
| 4. #26012495 | C2 | semidirect |
| 46. Q8×C173 | M16 | semidirect |
| 65. C173 | #2991 | semidirect |
| 102. Q8 | #14583836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13063443 | 2 |
| #26012525 | 2 |
| #26012510 | 2 |
| #26012495 | 2 |
| C4×#14583827 | 2 |
| #2991 | 173 |